Alligations or Mixtures
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Q.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup.

What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

 A.

7/11

 B.

6/7

 C.

1/5

 D.

2/7

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Solution:
Option(C) is correct

Suppose the vessel initially contains 8 litres of liquid.

Let $ x $ litres of this liquid be replaced with water then quantity of water in new mixture

$=3-\dfrac{3x}{8}+x$ litres

Quantity of syrup in new mixture $ =5-\dfrac{5x}{8} $ litres

After replacement, the quantity of water and syrup is same in the new mixture.

Therefore,

\begin{align*}
3-\dfrac{3x}{8}+x &= 5-\dfrac{5x}{8}\\
\Rightarrow 5x+24 &=40-5x\\
\Rightarrow 10x &=16\\
\Rightarrow x &=\dfrac{8}{5}
\end{align*}

So part of the mixture replaced,

$ =\dfrac{8}{5}\times \dfrac{1}{8} = \dfrac{1}{5}$


(9) Comment(s)


Abhijeet
 ()

This question can be solved verbally...

3k parts of water and 5k parts of syrup is present

total volume of final mixture is the same as it was before as the volume is just replaced

so to get 1:1 ratio

the final mixture can be 4k parts water and 4k parts syrup

i.e. 1 part of syrup is taken and replaced with 1 part of water

1 part of syrup is 1k/5k i.e.what we need/what we have in total

or it can also be said as 1/5th part of 5k is removed..



Deepak
 ()

Mix replaced is 8/5L. Which is 1/5 of total mixture I. E 8 l. In simple total mix is 20 and replace part is 5 than . replace part is 1/4 of total mix.


ABHIJEET
 ()

dont know what u saying bro..but it definitely is out of this world


Chakarya
 ()

Syrup part is only getting added with water mixture. So,

3/8 + 5x/8 = 1/2

(Water in mix + Syrup getting added with water) = Half of water or syrup

Solving for x, we get x = 1/5



Kritarth
 ()

why the answer 8/5 has been multiplied with 1/8 ? please explain...thank u


Smart
 ()

8 by 5 litre mixure out of 8 litre initial solution is replaced that is 1 by 5 part of initial mixture


Div
 ()

please explain it again



Parul
 ()

plzz explain it...



Sim
 ()

not getting it........Sad